Archive for April, 2012

Your child's genome before the 2nd trimester?

By Razib Khan | April 30, 2012 7:42 pm

A long piece in Slate, Will Gattaca come True?:

When Lo licensed his technology to Sequenom, he stipulated that it could not be used for sex selection. Rabinowitz says Natera won’t test for sex at this point, either. But how long such provisions will hold is unclear. Meanwhile, NIPD’s reach is expanding as the technology used to analyze cffDNA improves. In December 2010, Lo published a paper in Science Translational Medicine showing that in principle, at least, scientists can piece together the entire fetal genome from cffDNA. Lo says that exceeded even his own expectations: “If you asked me prior to 2008, I would have probably said that was science fiction.”

At the time his paper was published, the process cost $200,000. Now, with the cost of DNA sequencing dropping faster than that of computing power, he estimates the bill may come to one-tenth of that—still expensive, but no doubt tempting for some parents. Lo wagers complete fetal genome testing might be widely available in a clinical setting within a decade. What fetal genes might one day suggest about a baby’s eye color, appearance, and intellectual ability will be useful to parents, not insurers. But with costs coming down and insurers interested in other aspects of the fetal genome, a Gattaca-like two-tiered society, in which parents with good access to health care produce flawless, carefully selected offspring and the rest of us spawn naturals, seems increasingly plausible.

First, it’s rather crazy that as we live and breathe it is on the order of $20,000 to get a genome of your unborn children! I say on the order because no one knows, and I assume that they’re being optimistic here for media consumption. We plan to get screening for karyotype scale issues for our next child, so I keep track of this area with some interest.

All that being said, without pre-implantation genetic diagnosis it’s going to be very unlikely that you will get the “perfect child,” barring gene therapy. I may be unimaginative, but I can’t see the actionable use of a relatively dense genotype, let alone a full genome, at this stage once you eliminate the risks of very problematic diseases. I suppose at this point I can divulge that I tried to get my daughter’s genetic material from a c.v.s., so she could get typed while she was in utero, but that was mostly for the “wow!” factor (for what it’s worth, it’s really hard to get genetic material back from large biomedical firms).

Finally, I don’t find the beating-around-the-bush about “trick ethical questions” that is par for the course of these sorts of pieces useful. The reality is that most of the public finds this aspect of personal genomics “scary.” You don’t need to genuflect to it, just accept it as a given. Rather, lay out the issues in explicit detail, and let the people make their own judgement.

CATEGORIZED UNDER: Personal Genomics
MORE ABOUT: Personal genomics

Redefining "impact factor"

By Razib Khan | April 30, 2012 12:50 am

In rereading the paper on Pygmy height genetics, I noticed that PLoS had rolled out some nice new metrics. To my shock this paper, which I think is a moderately big deal, had less than 1,000 views, and only ~150 PDF downloands! This is going to change, but it still shocks me. With all due respect to my statistical geneticist friends, but this isn’t an abstruse methods paper debuting a new technique!

I decided to check on an older paper which has been rather influential, A Map of Recent Positive Selection in the Human Genome, from 2006. Here are the metrics:

Good? Bad? What do you think? Did you expect more downloads in the past 6 years?


Pygmies: "old" populations, and a new "look" (?)

By Razib Khan | April 30, 2012 12:32 am

Over the years one issue that crops up repeatedly in human evolutionary genetics and paleoanthropology (or more precisely, the popular exposition of the topics in the media) is the idea that is that “population X are the most ancient Y.” X will always refer to a population within a larger set, Y, which is defined by relative marginalization or retention of older cultural folkways. So, for example, I have seen it said that the Andaman Islanders are the “most ancient Asian population.” Why? The standard model for a while now has been that non-Africans derive from a line of Africans which left the ancestral continent 50 to 100 thousand years ago, and began to diversify. Presumably Andaman Islanders have ancestry which goes back to this original dispersion, just as Europeans and Chinese do (revisions which suggest that Aboriginals may have been part of an earlier wave, still put the Andamanese in the second wave). The reason that the Andaman populations are termed ancient is pretty straightforward: they’re Asia’s last hunter-gatherers, literally chucking spears at outsiders. An ancient lifestyle gets conflated with ancient genetics.

This is a much bigger problem with the hunter-gatherers of Africa, the Pygmies, Hadza, and Bushmen. The reason is that these populations are of particular interest because they seem to have diverged from the rest of humanity rather early on. Both Y chromosomes and mtDNA confirmed this, and now autosomal analyses looking across the whole genome are confirming it. In other words, they’re basal to the rest of humanity. I believe this is moderately misleading. With the Bantu Expansion much of African genetic diversity disappeared. The hunter-gatherers seem exceptional long and bare branches on the phylogenetic tree because all their relatives are gone!

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Rise and fall of celebutantes

By Razib Khan | April 29, 2012 8:46 pm

Kim Kardashian was at the White House Correspondents Association Dinner. Wow. But it made me wonder whatever happened to Paris Hilton? Did she drop off the face of the earth? Here’s Google Trends:

The bottom panel is news, the top panel public searches. The media seems to exhibit some latency in relation to the public, but at this point they both agree: Paris is near a nobody.


Comparing American conservative Protestants & Muslims

By Razib Khan | April 29, 2012 8:09 pm

A few years ago a book came out, American Taliban: How War, Sex, Sin, and Power Bind Jihadists and the Radical Right. The title clearly was aimed to push copies, but the gist of the title has moderately wide circulation. The rough sketch is that conservative American Protestants are roughly equivalent to conservative Muslims. I have always held that this is a qualitatively misleading analogy. The reason is from all I can gather the socially views of mainstream American conservative Protestants are actually in the moderate range of opinion amongst Muslims. But apples-to-apples comparisons are rather difficult in this domain.

But then I realized that the World Values Survey could allow me to do exactly such comparisons. The method is simple. First, you can subsample the data sets, so I could look at Protestants in the United States who identified as political conservatives. I compared these to the view of Muslims in a selection of nations (the WVS doesn’t cover much of the world, and some questions are not asked in some countries).

The results below range from 1, never justifiable, to 10, always justifiable. There is some strangeness in the results below, but they show the general qualitative result: American conservative Protestants are in the main to the center or social liberal end of Muslim public opinion. They are not comparable at all to Muslim reactionaries.

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MORE ABOUT: Data, Public opinion

Her identity by descent made flesh

By Razib Khan | April 29, 2012 2:49 pm

As I have indicated before, my daughter has a family tree where everyone out to 0.25 coefficient of relatedness has been genotyped by 23andMe. This is convenient in many ways. Before, relatedness was a theory. Now relatedness can be ascertained on the genomic level. Sometimes this can lead to peculiar consequences. “On paper” my daughter is 1/8 Scandinavian. Or 12.5%. But truly the expected value is 13.5%! (weighting by contributions from each maternal grandparent). Still, this remains an expected value. I would need a large sample of Scandinavians from that locale to make a truly precise guess as to the genetic contribution. Similarly, though I come in at about ~15 percent East Asian, my daughter looks to be a bit more East Asian than you’d expect based on that value (i.e., closer to 8-8.5 percent; I run her genotype more than a dozen times now). This may be a bias in the methodology, or, more likely it is simply the sampling error from my genome (I contributed more East Asian segments in the chromosomes passed down).

In any case, 23andMe has a “family inheritance” feature which is very convenient. It illustrates visually chromosome by chromosome the extent to which two individuals match genomic segments. Presumably this is useful for those who are distant cousins, who may match on a segment here and there. Instead of just focusing on one base pair, A/C/G/T, the method looks at the correlations of bases across a sequence of the chromosome. Below are the visualizations for matches of each individual with my daughter, in sequence: father, mother, paternal grandfather, paternal grandmother, maternal grandfather, maternal grandmother, paternal uncle, paternal uncle, paternal aunt, and maternal uncle. And no, I don’t know why it has an XY in the plots. For those of you without a biological background I hope that this can help in getting across how Mendelism manifests in a concrete manner. And if you do have a biological background, you can infer from these matches other interesting information about the meiotic process.

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CATEGORIZED UNDER: Genetics, Genomics, Personal Genomics
MORE ABOUT: Personal genomics

Elizabeth Warren, Native American

By Razib Khan | April 29, 2012 9:42 am

Elizabeth Warren, Native American

It has come to my attention that Elizabeth Warren, who is running for a Senate seat in Massachusetts, claims Native American ancestry. This did not surprise me. Warren is from Oklahoma, where nearly 10% of the population claims some Native American ancestry. The problem, as it is, is that apparently Harvard claimed Warren as a minority faculty member during its periodical head counts. Warren “was told through family lore that her maternal parents were from the Cherokee and Delaware tribes.” This is a moderate problem: family lore often is inaccurate. And it also exhibits biases. Nevertheless, I do think we need to be careful about being too skeptical in this case, because of Warren’s roots in Oklahoma. A friend was told that his maternal grandmother was of part Oklahoma Choctaw background, and he had always dismissed this as romantic distortions made to fit 21st century preconceptions and preferences. But when he got his results back from 23andMe there was a notable “Asian” component, and the Native American relative finder came back positive. He asked me to look at his results more deeply, and it was pretty obvious that yes, he was part Native American, in actually the proportions that you would have expected.

But this doesn’t always work out. It seems the majority of white Americans who suspect Native American ancestry find none from what I can tell. Recently I received a copy of DNA USA: A Genetic Portrait of America. Here’s a section on Cherokee genetic results:

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CATEGORIZED UNDER: Personal Genomics
MORE ABOUT: Elizabeth Warren

Facing the ocean

By Razib Khan | April 28, 2012 11:35 pm

Halford Mackinder’s conceptualization of the world

With the recent publication of the paper on the archaeogenetics of Neolithic Sweden I feel like we’re nearing a precipice. That precipice overlooks lands of great richness, filled with hope. It’s nothing to fear. It is in short a total re-ordering of our conception of the recent human past, at minimum. The “pots not people” paradigm arose in archaeology over the past few generations due to both scholarly and ideological factors. The scholarly ones being that intellectuals of the 19th and early 20th century made assumptions of extremely tight correspondence between material and cultural characteristics, and demographic dynamics, which seem to have been false. Therefore, the rise of an Anglo-Saxon England and the marginalization of Celtic Britain to the western fringes was not just a cultural reality, but also a fundamentally racial one, as Germans replaced Celts in totality. The ideological problem is that this particular framework was take as a given by the Nazis during World War II, lending a bad odor to the

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MORE ABOUT: Agriculture

Iraq: the model that wasn't

By Razib Khan | April 28, 2012 11:13 pm

The magazine Foreign Policy recently had a “sex” issue out. This issue is particularly famous for Mona Eltahaway’s jeremiad against Arab male culture, and their attitudes toward women. Over at Charli Carpenter expresses some concern that the issue seemed so singularly focused on Arabs, as if women’s rights is a problem with particular salience for Arab Muslims. As it is, she admits that as a matter of truth it may be so, but still has qualms about essentialization.

Now, I like to think in terms of distributions, and don’t find essentialization particularly useful on a fundamental level. But, my personal observation is that the term ‘essentialization’ tends to be used when there are phenomena brought to light which make people uncomfortable. For example, I rarely hear essentialization being nearly a great a problem when talking about Republicans or Western Christian conservatives.

But it does make to wonder: how bad are Arab countries when it comes to women’s rights? Let’s look at the World Values Survey. There are two questions in the survey which have a lot of normative baggage:

– If jobs are scarce: men should have more right to a job than women

– It is an essential characteristic of democracy that women have the same rights as men

As a matter of pedantic accuracy obviously it is not an essential characteristic of democracy that women and men have the same rights. Ancient Athens and America before the 1920s are generally considered democracies. But, the question is a rough gauge of attitudes toward male and female legal equality. I relabeled these questions as “economic” and “legal” equality. They are given as percentages, so I converted the categories into numbers, and then took the weighted average. These two indices measure the two dimensions of equality, with higher values favoring more equality. Below I generated a scatterplot showing the relationship between the two (naturally positively correlated). I’ve also attached table data after the figure.

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MORE ABOUT: Arabs, Sex

Handicap breeds excellence?

By Razib Khan | April 28, 2012 1:13 am

There’s a wide-ranging story in LA Weekly on the decline of 35mm film. It covers a lot of angles, but this one issue jumped out at me:

No wonder, then, that directors like Christopher Nolan worry that if 35mm film dies, so will the gold standard of how movies are made. Film cameras require reloading every 10 minutes. They teach discipline. Digital cameras can shoot far longer, much to the dismay of actors like Robert Downey Jr. — who, rumor has it, protests by leaving bottles of urine on set.

“Because when you hear the camera whirring, you know that money is going through it,” Wright says. “There’s a respectfulness that comes when you’re burning up film.”

This particular variant of critique of new technologies is very old. It is famously well known that writing and printing both ushered in warnings that these were simply crutches, and might diminish mental acuity. But I’m 99% sure that when bow & arrow become common, some hunters warned that the skills and traditions associated with the atlatl would decay. The piece highlights some genuine advantages of analog over digital. I do not think making filming more difficult is an advantage, to state the obvious.

MORE ABOUT: Technology

America: as if it is 1970

By Razib Khan | April 26, 2012 11:19 pm

I noticed that The Washington Post had an article up, Number of biracial babies soars over past decade, based on 2010 Census data. I was immediately curious if my expectations were correct in this case, because the term “biracial” has a very specific connotation. That is, there are two races, and in America that is black and white. If you want to break out of this old dichotomy you usually say multiracial. This paradigm has a historical valence, because the “race issue” in America has traditionally been in black and white, with a minor secondary role for native populations. I say traditionally, because by any measure the minority of America’s minorities are now black.

And sure enough the article does focus on the black-white dimension, with honorable mention for a woman of Asian heritage. But it is notionally based on the Census, right? It was easy to find the press release on the Census website. Here is the table accompanying it:


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MORE ABOUT: Culture, Interracial

The last days of Grendel

By Razib Khan | April 26, 2012 10:27 pm

A new paper in Science has just been published which in its broad outlines has been described in conference presentations. When examining the autosomal genetic variation of three individuals of the hunter-gatherer Pitted Ware Culture (PWC), and one of the agriculturalist Funnel Beaker Culture (TRB), the authors found that the two groups were sharply differentiated. The number of SNPs was on the order of 10,000 or so if I read the methods correctly. This is rather thin for studying contemporary within European population differences (~100,000 or more seems to be safe), in particular using hypothesis based clustering algorithms (it seems more manageable for PCA). But the findings are strong enough that I think we shouldn’t discount them. The most fascinating aspect of the results is that while the PWC seem to exhibit affinities with Northern and Northeastern Europeans, the TRB individual seems more similar to extant Southern Europeans!

Others have already commented extensively on the results. Keeping in mind the small sample sizes, limitation of comparisons, and the relatively thin marker set, I think the primary result we can take away from these findings is that old models of pure cultural and demographic diffusion are false. By this, I mean that prior debates which culminated in the early aughts on the “Paleolithic vs. Neolithic” contribution to the ancestry of modern Europeans were fundamentally premised on a demographic diffusion dynamic, whereby genes and ideas exhibited a continuous flow across a flat and featureless landscape. On the contrary, the basic outlines we are seeing here is that the human past exhibited spatial and temporal discontinuity. And why should this surprise us? There is no dialect continuum between Spanish and Chinese across Eurasia. Rather, broad language families are sharply differentiated from each other at zones of contact. Though there are theoretical reasons why the variation in genes should be more clinal, the reality remains that cultural parameters are going to shape the outlines of genetic variation, and those parameters are discontinuous.

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CATEGORIZED UNDER: Agriculture, Anthroplogy
MORE ABOUT: Agriculture, Europe

Types of genetics

By Razib Khan | April 25, 2012 11:06 pm
  • Molecular genetics
  • Developmental genetics
  • Population genetics
  • Quantitative genetics
  • Phylogenetics

Thoughts? Recently had a discussion whether phylogeneticists considered themselves geneticists (qualified “no”). Quantitative genetics really evolved out of biometrics, which actually opposed Mendelian genetics. You can construct quantitative genetics from Mendelian first principles, but it is not necessary. As for population vs. molecular, ask each group what they mean by “gene.” Modern developmental geneticists seem to be closely aligned with molecular geneticists.

MORE ABOUT: Genetics

Leaning the wrong way?

By Razib Khan | April 24, 2012 11:06 pm

Many of the people I socialize with in “real life” have a biological sciences background. That being said, a relatively deep understanding of ncRNA does not give you any better sense of behavior genetics than the person off the street. And of course when you have a small child conversation often goes in the direction of how you want to raise the child so as to maximize their outcomes. Setting aside the particular normative valence of those outcomes, I am always struck by the power people think parents have over their child’s life path. This is not to say parents don’t have power. There are many young people who have college degrees because of parental expectations. Or, perhaps more precisely the social expectations which the parents set in motion by selecting the milieu of one’s children. Yet so many times I’ve been in a conversation where the phrase “I lean toward nurture” has come up. These are not dogmatic “blank slate” individuals. Rather, they are simply falling back upon the null or default of our age.

But for me here is the irony: I think it is arguably the case today we live in a world where nurture matters far less in variation in outcome of exactly the people who ‘lean toward nurture.’ Let me repeat: when you remove environmental variation by providing a modicum of comfort , you are left with genetic variation! There were times in the past when ‘nurture,’ in other words the hand that environment dealt, was much more influential. And yet during those periods it was nature which was ascendant.

In 2004 the General Social Survey asked a question where respondents were asked to decide between “genes play major role in determining personality” and “experience determines personality.” For various reasons I do not think that the question was good, but, the responses are illustrative of the unanimity we’ve achieved in American society on some questions.

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MORE ABOUT: Nature vs. Nurture

One baby, alone on a PCA island

By Razib Khan | April 24, 2012 8:40 pm

A week ago I reported that according to 23andMe I’m 40% Asian, and she is 8% Asian (in the future if I say “she” without explanation, you know of whom I speak). Obviously something is off here. The situation resolved itself when I tuned my parameters and increased my sampled populations in Interpretome. By now I’ve already done the estimates of recombination on the chromosomes which came together to produce her, and the realized value of 8 percent instead of 20 percent “Asian” simply can not be due to a particular set of unlikely crossing over events. From what I can gather it seems like ancestry painting should be viewed as a qualitative rather than a quantitative assessment. This sounds really strange when you are given percentages, but the results are strange, and obviously wrong too often in terms of the specific values.

Here’s an admixture plot which shows more realistically informative values:

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CATEGORIZED UNDER: Anthroplogy, Personal Genomics
MORE ABOUT: Personal genomics

The world is as it should be in personal genomics

By Razib Khan | April 23, 2012 11:04 pm

I’ve been having some fun with my daughter’s personal genomics. You see, she has her whole pedigree out to r = 1/4. So, for example, contributions from her grandparents seem to be about on this order:

Paternal grandfather = 0.28
Paternal grandmother = 0.22
Maternal grandfather = 0.23
Maternal grandmother = 0.27

I’ve also calculated the number of recombinations which occurred leading up to the gametes which fused to create her. That will be for a future post. But here let’s confirm that she is not inbred. I used plink for this. Here is the description of the command:

Given a large number of SNPs, in a homogeneous sample, it is possible to calculate inbreeding coefficients (i.e. based on the observed versus expected number of homozygous genotypes).

The estimate of F can sometimes be negative. Often this will just reflect random sampling error, but a result that is strongly negative (i.e. an individual has fewer homozygotes than one would expect by chance at the genome-wide level) can reflect other factors, e.g. sample contamination events perhaps.

My main confusion here was which population I should select? Should I select GIH (HapMap Gujaratis?) or CEU (Utah whites)? I ended up on the TSI sample (Tuscans) as a fake compromise. And of course, because she is mixed-race the results came out very negative, as she had way less homozygosity than would be “expected” from the population wide statistic. I also added an inbred friend (his parents are first cousins) as a “control.” Below are two plots which show the result.

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CATEGORIZED UNDER: Personal Genomics

An algorithm is just an algorithm

By Razib Khan | April 23, 2012 9:48 pm

In the comments below:

You should include a Moroccan or otherwise native North African sample. Without a North African sample West Africans act as proxy for some of that North African ancestry that does exist in Iberia, specially the Western third (Portugal, Galicia, Extremadura, León, etc.) Doing that your analysis would become more precise and you could make better informed claims.

I was reading through all the entry and there was no mention to the rather surprising notable West African component in Iberians other than Basques. For my somewhat trained eye it is clear that this is a proxy for North African ancestry and not directly West African ancestry. This is demonstratedly also the case in Canary Islands, at least to a large extent, and, by extension in Cuba (which is nearly identical to your average Canarian), at least Cuba-1. Cuba-2 seems actually admixed at low levels and both seem to have some Amerindian ancestry not existent in Spain.

This is a fair point. I switched computers recently, and the Behar et al. data set I had seems to have become corrupted. So I snatched the Mozabites from the HGDP, and removed the Gujaratis from the previous run. I also added Russians, Druze, and some extra Amerindian groups. At K = 7 this pattern jumped out:

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Paternity most assured

By Razib Khan | April 23, 2012 12:32 am

The myth that 10 percent of children the product of ‘non-paternity events’ is rather persistent. I have no idea why, but I do know that even biologists accept it. But how we can we continue to accept this when surnames can provide population genetic information 400 years after the fact? The population of Belgium is famously divided between Latinate Walloons and Germanic Flemings. But is notable that a substantial number of Flemings carry surnames of clear Romance origin. This is in large part due to acculturation. Nevertheless, even 400 years after the largest of the migration and assimilation events males with Romance-origin surnames reflect their genetic background:


If non-paternity events occurred at a rate of 1 out of 10 the correlation between surnames and genetic lineage would have been decoupled long ago. These results have been confirmed in other societies. I predict that low non-paternity rates will also be confirmed in China; as that nation has a long history of surnames. Of course, one might posit a scenario where males who are the products of non-paternity events tend to be less fit than those who are not, so over the long term these estimates based on present day Y chromosomal lineages may not be appropriate reflective of the frequency of events at some point in the past.

MORE ABOUT: Non-paternity

The culture that is Microsoft

By Razib Khan | April 23, 2012 12:03 am

Frustration, Disappointment And Apathy: My Years At Microsoft:

Large companies have overheads, a necessary evil, you say. Overheads need to be managed. And managed they are: Group Managers, Program managers, General managers, together with ‘Senior’ flavours of those and a whole new breed of directors, stakeholders, business owners, relationship leads coupled with their own countless derivatives.

All those meeting-goers are not making anything. Deciding upon and making something is hard. And if this onerous activity has to be done, then hire external consultants for it. It’s easier and less risky.

There is no creative tension, no vision these days. Left to Microsoft’s hands we’d still be toiling on overheating Vista desktops.

This company is becoming the McDonalds of computing. Cheap, mass products, available everywhere. No nutrients, no ideas, no culture. Windows 8 is a fine example. The new Metro interface displays nonstop, trivial updates from Facebook, Twitter, news sites and stock tickers. Streams of raw noise distract users from the moment they login.

The rise of sclerotic bureaucratic intermediaries isn’t just a problem with Microsoft. Remember when parasitic squid were generating 40 percent of the economy’s profits? It’s no better in academia:

MORE ABOUT: Microsoft

A deeper dive analysis of two Cubans

By Razib Khan | April 22, 2012 11:42 pm

About a week ago I put up a post put on an analysis of a paper which reported on the ancestral make up of 50 Cubans (as well as assorted other Hispanic/Latino groups). One aspect of the paper which was somewhat notable is that 1 out of 3 Cubans were 90 percent or more European in ancestry. The notability of this is that is that 5 out of 6 Cuban Americans identify as white. That is, of European ancestry. The main caveat here is that these Cubans were sampled from New York City, and to a lesser extent the Midwest. The fact of non-European admixture in putatively white European individuals from Latin America is not surprising. Our prior expectation should be that the admixture is non-trivial, though not preponderant. For example, the majority of the white population of Argentina has Amerindian ancestry (or, more precisely ~15 percent of the aggregate ancestry of Argentineans is Amerindian). At least notionally Cuba is a much more racially mixed culture than Argentina, so non-white admixture in even white Cubans is not surprising.

Based on the above paper (and the data which you can find on other Latin American whites), as well as the genotyping of two Cuban American acquaintances, I asserted that on the order of ~10 percent of the ancestry of the average white Cuban was going to be African. Naturally this prompted some objections. Some of the individuals were not too polite. I think the primary issue that I have to be honest about this is this: I don’t really care too much about the topic on a visceral level. Now, I’m interested in it. And the specific cases illuminate a greater whole, which comments upon various demographic and population genetic dynamics. But I don’t have a strong investment in the specific instance of the particular ancestral quanta of Cubans, or any other group really.

Second, there was some objection to punctilious attention to scientific methodology, such as representativeness and sample size. This is a serious objection in the abstract, but the reality is that a generation of genomics has been performed with lineages as unrepresentative as “Utah whites.” Science and knowledge seeking is frankly operationally an ad hoc and sloppy process, without great attention to the book of proper scientific methodology. When we don’t have much information, any extra information is often useful, so long as we keep in mind the error that this introduces into the process.

All that being said, one commenter brought to my attention an interesting paper. It reports 6 percent African ancestry in a very large population of white Havana Cubans. The main downside is that they used only 60 SNPs, as opposed to the 60,000 SNPs in the above study. Of course those 60 SNPs would be “ancestrally informative,” but at 6 percent vs. 10 percent (my prior estimate), I’m not sure that I should totally trust the precision and update my values. But I think that nevertheless this study converges upon the same qualitative result: white Cubans, like white Latin Americans in generally, seem to usually exhibit non-trivial amounts of non-European ancestry.

But in the interests of moving the discussion forward, the commenter who brought the above paper to my attention supplied two 23andMe genotypes of Cuban Americans: herself and her husband. I will now refer to her as “Cuba 1” and her husband as “Cuba 2.” I created a pooled data set of the following populations:

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